The Constraint Satisfaction Problem I mentioned is similar to CNF-SAT: A variable can take values from some finite domain $D$ where $d=|D|$. A literal of variable $x$ is an expression of the form $x\neq c$, where $c\in D$. A constraint is a disjunction of literals, and a formula is a conjunction of constraints. 
For example, let $D=\{0,1,2\}$, then $F=(x_1\neq 1\vee x_2\neq 0\vee x_3\neq 2)\wedge (x_2\neq 0\vee x_4\neq 2\vee x_5\neq 1)\wedge (x_3\neq 2\vee x_5\neq 0)$ is a formula with $6$ variables and $3$ constraints. 
If we assign $x=0$, then literal $x\neq 0$ evaluates to false, and literals $x\neq 1$ and $x\neq 2$ evaluate to true. A formula is satisfiable if there is an assignment that makes the formula evaluate to true. 
In CSP, the task is to decide whether the input formula is satisfiable.

CSP with $n$ variables ranging over a domain of $d$ values can be solved in $O^*(d^n)$ time (the $O^*(\cdot)$ notation omits polynomial factor) by enumerating all possible assignments.
Since CSP is a generalization of CNF-SAT, I wonder if there is any hypothesis about the worst-case runtime like SETH, e.g., CSP can not be solved in $O^*(d^{(1-\epsilon)n})$ time for any constant $\epsilon>0$?

Since CNF-SAT can be reduced to CSP with $d=2$, what I want to know is the case when $d\geq 3$.